Bandgap reference circuits traditionally have a bipolar transistor. A bandgap reference voltage is derived from the base-emitter voltage of the bipolar transistor and provided. However, at their base and emitter terminals bipolar transistors have parasitic resistances, which affect the base-emitter voltage on which the function of the bandgap reference circuit is based. This will be explained in more detail below on the basis of FIG. 4.
FIG. 4 shows a bipolar transistor with a parasitic base resistance Rb and a parasitic emitter resistance Re. The bipolar transistor is driven by a collector current Ic. The base-emitter voltage Ube of the bipolar transistor shown in FIG. 4 is defined as follows:
                              U          be                =                                            U              t                        ⁢                                                  ⁢                          ln              ⁡                              (                                                      I                    c                                                        I                    s                                                  )                                              +                                                    I                c                            ⁡                              (                                  1                  +                                      1                    β                                                  )                                      ⁢                                                  ⁢                          R              e                                +                                    I              c                        ⁢                          1              β                        ⁢                          R              b                                                          (        1        )            where Is is the reverse current of the bipolar transistor, and β is the current amplification of the bipolar transistor. From Formula (1), the effect of the parasitic base and emitter resistances on the base-emitter voltage can be seen. These parasitic resistances result in the corresponding bandgap reference circuit being affected by parasitic temperature coefficients, which can only be controlled with difficulty and consequently result in imprecision and uncertainty in the circuit production.
Since all the voltages which are derived from the parasitic resistances are also referred to the collector current Ic, the effect of the parasitic resistances on the base-emitter voltage can be seen as derived from a virtual compensating resistance Req at the emitter of the bipolar transistor, as is shown schematically in FIG. 5. For the base-emitter voltage Ube, the result, depending on the collector current Ic and compensating resistance Req, is:
                                                                        U                be                            =                                                                    U                    t                                    ⁢                                                                          ⁢                                      ln                    ⁡                                          (                                                                        I                          c                                                                          I                          s                                                                    )                                                                      +                                                      I                    c                                    ⁡                                      (                                                                                                                        β                            +                            1                                                    β                                                ⁢                                                  R                          e                                                                    +                                                                        R                          b                                                β                                                              )                                                                                                                          =                                                                    U                    t                                    ⁢                                                                          ⁢                                      ln                    ⁡                                          (                                                                        I                          c                                                                          I                          s                                                                    )                                                                      +                                                      I                    c                                    ⁢                                      R                    eq                                                                                                          (        2        )            Consequently, to remove the effect of the parasitic resistances, the aim must be to compensate for the effect of the compensating resistance Req (shown in FIG. 5) on the base-emitter voltage Ube. Traditionally, base-emitter interfaces are connected in series for this purpose.
For this purpose, in particular, constructing bandgap reference circuits in such a way that a temperature-proportional voltage, that is a voltage with a positive temperature coefficient, is added to a voltage which is inversely temperature-proportional and consequently has a negative temperature coefficient, in such a way that the resulting voltage has a negligible temperature coefficient, is known. The temperature-proportional voltage can be obtained as a voltage difference between two transistors which are operated with different current densities, whereas the voltage with the negative temperature coefficient is obtained as a voltage over a base-emitter interface.
The principle explained above will be described in more detail below with reference to FIG. 6, wherein in FIG. 6 a circuit arrangement called a Widlar bandgap reference circuit is shown.
The circuit arrangement shown in FIG. 6 consists essentially of a temperature-proportional first circuit section 1, which can also be called the PTAT (“proportional to absolute temperature”) circuit section, and an inversely temperature-proportional second circuit section 2, which can be called the IPTAT (“inversely proportional to absolute temperature”) circuit section. The first circuit section 1 includes two bipolar transistors Q1 and Q2, which are connected to each other as shown in FIG. 6. The bipolar transistors Q1 and Q2 are also connected to resistors Rbias, Rt1 and Rt2, as shown in FIG. 6. The first circuit section 1 generates a temperature-proportional current, which flows via the bipolar transistor Q2 and resistor Rt2 and generates a voltage UR12, which is proportional to the absolute temperature, there. The second circuit section 2 includes a bipolar transistor Q3, the base-emitter voltage UbeQ3 of which is inversely proportional to the absolute temperature. The output of the bandgap reference circuit is connected to the two circuit sections 1, 2 in such a way that the bandgap reference voltage Ubg which can be tapped there is defined by the sum of the voltages UR12 and UbeQ3.
Irrespective of the fact that using the bandgap reference circuit shown in FIG. 6, a bandgap reference voltage with a mostly negligible temperature coefficient can be generated, the parasitic resistances which were explained above on the basis of FIGS. 4 and 5 are still included in the circuit, and because of their temperature coefficients they affect the base-emitter voltages of the relevant bipolar transistors and consequently the bandgap reference voltage of the entire circuit.